Game

本文链接：https://blog.youkuaiyun.com/u014733623/article/details/46238859

本文介绍了一个游戏中的胜负预测算法，游戏中两名玩家轮流从指定盒子中移动卡片到另一个盒子，获胜者为最后能进行合法移动的一方。文章分析了游戏规则，并提供了一种基于Nim游戏的解决方案。

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Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 435 Accepted Submission(s): 288

Problem Description

Bob and Alice are playing a new game. There are n boxes which have been numbered from 1 to n. Each box is either empty or contains several cards. Bob and Alice move the cards in turn. In each turn the corresponding player should choose a non-empty box A and choose another box B that B<A && (A+B)%2=1 && (A+B)%3=0. Then, take an arbitrary number (but not zero) of cards from box A to box B. The last one who can do a legal move wins. Alice is the first player. Please predict who will win the game.

Input

The first line contains an integer T (T<=100) indicating the number of test cases. The first line of each test case contains an integer n (1<=n<=10000). The second line has n integers which will not be bigger than 100. The i-th integer indicates the number of cards in the i-th box.

Output

For each test case, print the case number and the winner's name in a single line. Follow the format of the sample output.

Sample Input

2
2
1 2
7
1 3 3 2 2 1 2

Sample Output

Case 1: Alice
Case 2: Bob

题意：按照题目给定的A和B的要求，每次从A向B中转移任意数量的石子。最后不能操作的负。

思路：1.余0的箱子中的卡只能移到余3里，余3的箱子只能移到余0里。最终箱子编号为3；
2.余2的箱子中的卡只能移到余1里，余1的箱子只能移到余2里。最终箱子编号为1；
3.余4的箱子中的卡只能移到余5里，余5的箱子只能移到余4里。最终箱子编号为4；

因为最后不能移动的箱子为1,3,4，所以，%6=0,2,5的步数为奇数。将所有奇数的做Nim即可。

AC代码如下：

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
int T,t,n,m;
int main()
{
    int i,j,k,S;
    scanf("%d",&T);
    for(t=1;t<=T;t++)
    {
        scanf("%d",&n);
        S=0;
        for(i=1;i<=n;i++)
        {
            scanf("%d",&k);
            if(i%6==0 || i%6==2 || i%6==5)
              S^=k;
        }
        if(S==0)
          printf("Case %d: Bob\n",t);
        else
          printf("Case %d: Alice\n",t);
    }
}